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A new friction factor relationship for fully developed pipe flow

Published online by Cambridge University Press:  17 August 2005

B. J. McKEON ,
M. V. ZAGAROLA  and
A. J. SMITS
B. J. McKEON
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-0710, USA Present address: Department of Aeronautics, Imperial College, London SW7 2AZ, UK.
M. V. ZAGAROLA
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-0710, USA Present address: Creare Inc, Etna Road Box 71 Hanover, New Hampshire 03755, USA.
A. J. SMITS
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-0710, USA
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Abstract

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The friction factor relationship for high-Reynolds-number fully developed turbulent pipe flow is investigated using two sets of data from the Princeton Superpipe in the range $31 \,{\times}\, 10^3 \,{\le}\,\hbox{\it Re}_D \,{\le}\, 35 \,{\times}\, 10^6$. The constants of Prandtl's ‘universal’ friction factor relationship are shown to be accurate over only a limited Reynolds-number range and unsuitable for extrapolation to high Reynolds numbers. New constants, based on a logarithmic overlap in the mean velocity, are found to represent the high-Reynolds-number data to within 0.5%, and yield a value for the von Kármán constant that is consistent with the mean velocity profiles themselves. The use of a generalized logarithmic law in the mean velocity is also examined. A general friction factor relationship is proposed that predicts all the data to within 1.4% and agrees with the Blasius relationship for low Reynolds numbers to within 2.0%.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 538 , 10 September 2005 , pp. 429 - 443
Copyright
© 2005 Cambridge University Press